Global existence of classical solutions to a cross-diffusion predator–prey system with a free boundary

Abstract

This paper is concerned with a cross-diffusion predator–prey system with a free boundary over a one-dimensional habitat. The free boundary shows the spreading front of the prey and predator which implies that the velocity of the expanding front is proportional to the gradients of the prey and predator. By the contraction mapping principle, $$L^{p}$$ estimates and Schauder estimates of parabolic equations, the local and global existence and uniqueness of classical solutions are established for this system.